A thought experiment or Gedankenexperiment (from German) considers some hypothesis, theory,[1] or principle for the purpose of thinking through its consequences. Given the structure of the experiment, it may or may not be possible to actually perform it, and if it can be performed, there need be no intention of any kind to actually perform the experiment in question.

The common goal of a thought experiment is to explore the potential consequences of the principle in question: "A thought experiment is a device with which one performs an intentional, structured process of intellectual deliberation in order to speculate, within a specifiable problem domain, about potential consequents (or antecedents) for a designated antecedent (or consequent)" (Yeates, 2004, p. 150).

The ancient Greek δείκνυμι(transl.: deiknymi), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics,[2] where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. Perhaps the key experiment in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. This is widely thought[3] to have been a straightforward physical demonstration, involving climbing up the Leaning Tower of Pisa and dropping two heavy weights off it, whereas in fact, it was a logical demonstration, using the 'thought experiment' technique. The 'experiment' is described by Galileo in Discorsi e dimostrazioni matematiche (1638) (literally, 'Discourses and Mathematical Demonstrations') thus:

Salviati. If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion?

Simplicio. You are unquestionably right.

Salviati. But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than ' the lighter one, I infer that the heavier body moves more slowly.[4]

Although the extract does not convey the elegance and power of the 'demonstration' terribly well, it is clear that it is a 'thought' experiment, rather than a practical one. Strange then, as Cohen says, that philosophers and scientists alike refuse to acknowledge either Galileo in particular, or the thought experiment technique in general for its pivotal role in both science and philosophy. (The exception proves the rule — the iconoclastic philosopher of science, Paul Feyerabend, has also observed this methodological prejudice.[5])

Instead, many philosophers prefer to consider 'Thought Experiments' to be merely the use of a hypothetical scenario to help understand the way things actually are.

Thought experiments have been used in a variety of fields, including philosophy, law, physics, and mathematics. In philosophy, they have been used at least since classical antiquity, some pre-dating Socrates. In law, they were well-known to Roman lawyers quoted in the Digest.[6] In physics and other sciences, notable thought experiments date from the 19th and especially the 20th century, but examples can be found at least as early as Galileo.

Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the Latin-German mixed term Gedankenexperiment (lit. thought experiment) circa 1812.[7] Ørsted was also the first to use its entirely German equivalent, Gedankenversuch, in 1820.

Much later, Ernst Mach used the term Gedankenexperiment in a different way, to denote exclusively the imaginary conduct of a real experiment that would be subsequently performed as a real physical experiment by his students.[8] Physical and mental experimentation could then be contrasted: Mach asked his students to provide him with explanations whenever the results from their subsequent, real, physical experiment differed from those of their prior, imaginary experiment.

The English term thought experiment was coined (as a calque) from Mach's Gedankenexperiment, and it first appeared in the 1897 English translation of one of Mach’s papers.[9] Prior to its emergence, the activity of posing hypothetical questions that employed subjunctive reasoning had existed for a very long time (for both scientists and philosophers). However, people had no way of categorizing it or speaking about it. This helps to explain the extremely wide and diverse range of the application of the term "thought experiment" once it had been introduced into English.

Thought experiments, which are well-structured, well-defined hypothetical questions that employ subjunctive reasoning (irrealis moods) – "What might happen (or, what might have happened) if . . . " – have been used to pose questions in philosophy at least since Greek antiquity, some pre-dating Socrates (see Rescher 1991). In physics and other sciences many famous thought experiments date from the 19th and especially the 20th Century, but examples can be found at least as early as Galileo.

In thought experiments we gain new information by rearranging or reorganizing already known empirical data in a new way and drawing new (a priori) inferences from them or by looking at these data from a different and unusual perspective. In Galileo’s thought experiment, for example, the rearrangement of empirical experience consists in the original idea of combining bodies of different weight.[10]

Thought experiments can produce some very important and different outlooks on previously unknown or unaccepted theories. However, they may make those theories themselves irrelevant, and could possibly create new problems that are just as difficult, or possibly more difficult to resolve.

In terms of their practical application, thought experiments are generally created in order to:

challenge the prevailing status quo (which includes activities such as correcting misinformation (or misapprehension), identify flaws in the argument(s) presented, to preserve (for the long-term) objectively established fact, and to refute specific assertions that some particular thing is permissible, forbidden, known, believed, possible, or necessary);

Scientists tend to use thought experiments in the form of imaginary, "proxy" experiments which they conduct prior to a real, "physical" experiment (Ernst Mach always argued that these gedankenexperiments were "a necessary precondition for physical experiment"). In these cases, the result of the "proxy" experiment will often be so clear that there will be no need to conduct a physical experiment at all.

Scientists also use thought experiments when particular physical experiments are impossible to conduct (Carl Gustav Hempel labeled these sorts of experiment "theoretical experiments-in-imagination"), such as Einstein's thought experiment of chasing a light beam, leading to Special Relativity. This is a unique use of a scientific thought experiment, in that it was never carried out, but led to a successful theory, proven by other empirical means.

The relation to real experiments can be quite complex, as can be seen again from an example going back to Albert Einstein. In 1935, with two coworkers, he published a famous paper on a newly created subject called later the EPR effect (EPR paradox). In this paper, starting from certain philosophical assumptions,[11] on the basis of a rigorous analysis of a certain, complicated, but in the meantime assertedly realizable model, he came to the conclusion that quantum mechanics should be described as "incomplete". Niels Bohr asserted a refutation of Einstein's analysis immediately, and his view prevailed.[12][13][14] After some decades, it was asserted that feasible experiments could prove the error of the EPR paper. These experiments tested the Bell inequalities published in 1964 in a purely theoretical paper. The above-mentioned EPR philosophical starting assumptions were considered to be falsified by empirical fact (e.g. by the optical real experiments of Alain Aspect).

Thus thought experiments belong to a theoretical discipline, usually to theoretical physics, but often to theoretical philosophy. In any case, it must be distinguished from a real experiment, which belongs naturally to the experimental discipline and has "the final decision on true or not true", at least in physics.

Prefactual (before the fact) thought experiments — the term prefactual was coined by Lawrence J. Sanna in 1998[18] — speculate on possible future outcomes, given the present, and ask "What will be the outcome if event E occurs?"

Counterfactual (contrary to established fact) thought experiments — the term counterfactual was coined by Nelson Goodman in 1947,[20] extending Roderick Chisholm's (1946) notion of a "contrary-to-fact conditional"[21] — speculate on the possible outcomes of a different past;[22] and ask "What might have happened if A had happened instead of B?" (e.g., "If Isaac Newton and Gottfried Leibnizhad cooperated with each other, what would mathematics look like today?").[23]

The study of counterfactual speculation has increasingly engaged the interest of scholars in a wide range of domains such as philosophy,[24] psychology,[25] cognitive psychology,[26] history,[27] political science,[28] economics,[29] social psychology,[30] law,[31] organizational theory,[32] marketing,[33] and epidemiology.[34]

Semifactual thought experiments — the term semifactual was coined by Nelson Goodman in 1947[36][37] — speculate on the extent to which things might have remained the same, despite there being a different past; and asks the question Even though X happened instead of E, would Y have still occurred? (e.g., Even if the goalie had moved left, rather than right, could he have intercepted a ball that was traveling at such a speed?).

(2) “[Using] suites of observational data and sophisticated numerical models in an effort to foretell the behavior or evolution of complex phenomena”.[39]

Although they perform different social and scientific functions, the only difference between the qualitatively identical activities of predicting, forecasting, and nowcasting is the distance of the speculated future from the present moment occupied by the user.[40] Whilst the activity of nowcasting, defined as “a detailed description of the current weather along with forecasts obtained by extrapolation up to 2 hours ahead”, is essentially concerned with describing the current state of affairs, it is common practice to extend the term “to cover very-short-range forecasting up to 12 hours ahead” (Browning, 1982, p.ix).[41][42]

The activity of hindcasting involves running a forecast model after an event has happened in order to test whether the model's simulation is valid.

In 2003, Dake Chen and his colleagues “trained” a computer using the data of the surface temperature of the oceans from the last 20 years.[44] Then, using data that had been collected on the surface temperature of the oceans for the period 1857 to 2003, they went through a hindcasting exercise and discovered that their simulation not only accurately predicted every El Niño event for the last 148 years, it also identified the (up to 2 years) looming foreshadow of every single one of those El Niño events.[45]

The activity of retrodiction (or postdiction) involves moving backwards in time, step-by-step, in as many stages as are considered necessary, from the present into the speculated past, in order to establish the ultimate cause of a specific event (e.g., Reverse engineering and Forensics).

Given that retrodiction is a process in which “past observations, events and data are used as evidence to infer the process(es) the produced them” and that diagnosis “involve[s] going from visible effects such as symptoms, signs and the like to their prior causes”,[47] the essential balance between prediction and retrodiction could be characterized as:

retrodiction : diagnosis :: prediction : prognosis

regardless of whether the prognosis is of the course of the disease in the absence of treatment, or of the application of a specific treatment regimen to a specific disorder in a particular patient.[48]

The activity of backcasting — the term backcasting was coined by John Robinson in 1982[50] — involves establishing the description of a very definite and very specific future situation. It then involves an imaginary moving backwards in time, step-by-step, in as many stages as are considered necessary, from the future to the present, in order to reveal the mechanism through which that particular specified future could be attained from the present.[51]

Backcasting is not concerned with predicting the future:

The major distinguishing characteristic of backcasting analyses is the concern, not with likely energy futures, but with how desirable futures can be attained. It is thus explicitly normative, involving 'working backwards' from a particular future end-point to the present to determine what policy measures would be required to reach that future.[52]

Within the framework of technological development, “forecasting” concerns the extrapolation of developments towards the future and the exploration of achievements which can be realized through technology in the long term. Conversely, the reasoning behind “backcasting” is: on the basis of an interconnecting picture of demands which technology has to meet in the future — “sustainability criteria” — to direct and determine the process that technology development must take and possibly also the pace at which this development process must be put into effect.

Backcasting [is] both an important aid in determining the direction technology development must take and in specifying the targets to be set for this purpose. As such, backcasting is an ideal search toward determining the nature and scope of the technological challenge which is posed by sustainable development, and it can thus serve to direct the search process toward new — sustainable — technology.

In philosophy, a thought experiment typically presents an imagined scenario with the intention of eliciting an intuitive or reasoned response about the way things are in the thought experiment. (Philosophers might also supplement their thought experiments with theoretical reasoning designed to support the desired intuitive response.) The scenario will typically be designed to target a particular philosophical notion, such as morality, or the nature of the mind or linguistic reference. The response to the imagined scenario is supposed to tell us about the nature of that notion in any scenario, real or imagined.

For example, a thought experiment might present a situation in which an agent intentionally kills an innocent for the benefit of others. Here, the relevant question is not whether the action is moral or not, but more broadly whether a moral theory is correct that says morality is determined solely by an action's consequences (See Consequentialism). John Searle imagines a man in a locked room who receives written sentences in Chinese, and returns written sentences in Chinese, according to a sophisticated instruction manual. Here, the relevant question is not whether or not the man understands Chinese, but more broadly, whether a functionalist theory of mind is correct.

It is generally hoped that there is universal agreement about the intuitions that a thought experiment elicits. (Hence, in assessing their own thought experiments, philosophers may appeal to "what we should say," or some such locution.) A successful thought experiment will be one in which intuitions about it are widely shared. But often, philosophers differ in their intuitions about the scenario.

Other philosophical uses of imagined scenarios arguably are thought experiments also. In one use of scenarios, philosophers might imagine persons in a particular situation (maybe ourselves), and ask what they would do.

The scenario presented in a thought experiment must be possible in some sense. In many thought experiments, the scenario would be nomologically possible, or possible according to the laws of nature. John Searle's Chinese room is nomologically possible.

Some thought experiments present scenarios that are not nomologically possible. In his Twin Earth thought experiment, Hilary Putnam asks us to imagine a scenario in which there is a substance with all of the observable properties of water (e.g., taste, color, boiling point), but which is chemically different from water. It has been argued that this thought experiment is not nomologically possible, although it may be possible in some other sense, such as metaphysical possibility. It is debatable whether the nomological impossibility of a thought experiment renders intuitions about it moot.

In some cases, the hypothetical scenario might be considered metaphysically impossible, or impossible in any sense at all. David Chalmers says that we can imagine that there are zombies, or persons who are physically identical to us in every way but who lack consciousness. This is supposed to show that physicalism is false. However, some argue that zombies are inconceivable: we can no more imagine a zombie than we can imagine that 1+1=3. Others have claimed that the conceivability of a scenario may not entail its possibility.

The use of thought experiments in philosophy has received other criticisms, especially in the philosophy of mind. Daniel Dennett has derisively referred to certain types of thought experiments such as the Chinese Room experiment as "intuition pumps", claiming they are simply thinly veiled appeals to intuition which fail when carefully analyzed. Another criticism that has been voiced is that some science fiction-type thought experiments are too wild to yield clear intuitions, or that any resulting intuitions could not possibly pertain to the real world.

^"[C]onjectures or hypotheses ... are really to be regarded as thought "experiments" through which we wish to discover whether something can be explained by a specific assumption in connection with other natural laws." —Hans Christian Ørsted("First Introduction to General Physics" ¶16-¶18, part of a series of public lectures at the University of Copenhagen. Copenhagen 1811, in Danish, printed by Johan Frederik Schulz. In Kirstine Meyer's 1920 edition of Ørsted's works, vol.III pp. 151-190. ) "First Introduction to Physics: the Spirit, Meaning, and Goal of Natural Science". Reprinted in German in 1822, Schweigger's Journal für Chemie und Physik36, pp. 458–488, as translated in Ørsted 1997, pp. 296–298

^Sanna, L.J., "Defensive Pessimism and Optimism: The Bitter-Sweet Influence of Mood on Performance and Prefactual and Counterfactual Thinking", Cognition and Emotion, Vol.12, No.5, (September 1998), pp.635-665. (Sanna used the term prefactual, in order to distinguish these sorts of thought experiment from both semifactuals and counterfactuals.)

^In 1748, when defining causation, David Hume referred to a counterfactual case: "…we may define a cause to be an object, followed by another, and where all objects, similar to the first, are followed by objects similar to the second. Or in other words, where, if the first object had not been, the second never had existed …" (Hume, D. (Beauchamp, T.L., ed.), An Enquiry Concerning Human Understanding, Oxford University Press, (Oxford), 1999, (7), p.146.)

^Cowan, R. & Foray, R., "Evolutionary Economics and the Counterfactual Threat: On the Nature and Role of Counterfactual History as an Empirical Tool in Economics", Journal of Evolutionary Economics, Vol.12, No.5, (December 2002), pp.539-562, etc.

^Not only did their hindcasting demonstrate that the computerized simulation models could predict the onset of El Niño climatic events from changes in the temperature of the ocean's surface temperature that occur up to two years earlier — meaning that there was now, potentially, at least 2 years' lead time — but the results also implied that El Niño events seemed to be the effects of some causal regularity; and, therefore, were not due to simple chance, or to some other “chaotic” event.

^"…We consider diagnostic inference to be based on causal thinking, although in doing diagnosis one has to mentally reverse the time order in which events were thought to have occurred (hence the term “backward inference”). On the other hand, predictions involve forward inference; i.e., one goes forward in time from present causes to future effects. However, it is important to recognize the dependence of forward inference/prediction on backward inference/diagnosis. In particular, it seems likely that success in predicting the future depends to a considerable degree on making sense of the past. Therefore, people are continually engaged in shifting between forward and backward inference in both making and evaluating forecasts. Indeed, this can be eloquently summarized by Kierkegaard's observation that, “Life can only be understood backwards; but it must be lived forwards” …"(Einhorn & Hogarth, 1982, p.24).

^While the problem presented in this short story's scenario is not unique, it is extremely unusual. Most thought experiments are intentionally (or, even, sometimes unintentionally) skewed towards the inevitable production of a particular solution to the problem posed; and this happens because of the way that the problem and the scenario are framed in the first place. In the case of The Lady, or the Tiger?, the way that the story unfolds is so "end-neutral" that, at the finish, there is no "correct" solution to the problem. Therefore, all that one can do is to offer one's own innermost thoughts on how the account of human nature that has been presented might unfold ? according to one's own experience of human nature ? which is, obviously, the purpose of the entire exercise. The extent to which the story can provoke such an extremely wide range of (otherwise equipollent) predictions of the participants' subsequent behaviour is one of the reasons the story has been so popular over time.

Hempel, C.G., "Typological Methods in the Natural and Social Sciences", pp. 155–171 in Hempel, C.G. (ed.), Aspects of Scientific Explanation and Other Essays in the Philosophy of Science, The Free Press, (New York), 1965.